论文标题
古典组矩阵模型和普遍关键性
Classical group matrix models and universal criticality
论文作者
论文摘要
我们研究了特殊正交和符号群体的总（WITTEN）wADIA统一基质模型的概括。我们显示使用标准的库仑气体处理 - 使用一个耦合恒定的间隙相位的路径积分形式，并为间隙阶段进行分解技术 - 在$ n $限制中，自由能归一化模量仪表仪的平方量表等级的平方是不单亲案例的两倍。然后，使用广义的cauchy身份作为字符多项式，然后通过将该模型与基于Schur度量的随机分区联系起来，以任意数量的耦合常数来证明该相变的普遍性。
We study generalizations of the Gross--Witten--Wadia unitary matrix model for the special orthogonal and symplectic groups. We show using a standard Coulomb gas treatment -- employing a path integral formalism for the ungapped phase and resolvent techniques for the gapped phase with one coupling constant -- that in the large $N$ limit, the free energy normalized modulo the square of the gauge group rank is twice the value for the unitary case. Using generalized Cauchy identities for character polynomials, we then demonstrate the universality of this phase transition for an arbitrary number of coupling constants by linking this model to the random partition based on the Schur measure.
